A process and apparatus are disclosed in U.S. Pat. No. 3,857,436, by which production of single-crystal structural parts is achieved by means of a single-crystal seed crystal placed at the bottom of a casting mold. This process and apparatus has the disadvantage that the seed crystal surface is subjected to an aggressive atmosphere due to the evaporation of volatile components from the casting mold during the entire purification and warm-up time of the casting mold, which increases the risk of polycrystal growth, slip formation and a high concentration of crystal defects at least in the initial phase of crystal growth. Additionally, the conventional seed crystals usually have a large number of defects, i.e. are defect-rich and thereby disadvantageously tend toward polycrystalline growth. These disadvantages lead to a low reproducibility of the single-crystal cultivation and thus to high waste.